An Alternative Lambert-Type Distribution for Bounded Data

In this article, we propose a new two-parameter distribution for bounded data such as rates, proportions, or percentages. The density function of the proposed distribution, presenting monotonic, unimodal, and inverse-unimodal shapes, tends to a positive finite value at the lower end of its support,...

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Bibliographic Details
Main Authors: Héctor Varela, Mario A. Rojas, Jimmy Reyes, Yuri A. Iriarte
Format: Article
Language:English
Published: MDPI AG 2023-01-01
Series:Mathematics
Subjects:
Online Access:https://www.mdpi.com/2227-7390/11/3/667
Description
Summary:In this article, we propose a new two-parameter distribution for bounded data such as rates, proportions, or percentages. The density function of the proposed distribution, presenting monotonic, unimodal, and inverse-unimodal shapes, tends to a positive finite value at the lower end of its support, which can lead to a better fit of the lower empirical quantiles. We derive some of the main structural properties of the new distribution. We make a description of the skewness and kurtosis of the distribution. We discuss the parameter estimation under the maximum likelihood method. We developed a simulation study to evaluate the behavior of the estimators. Finally, we present two applications to real data providing evidence that the proposed distribution can perform better than the popular beta and Kumaraswamy distributions.
ISSN:2227-7390